Hi - this is something I've looked at in some detail in the past. An uncontrolled heat source (which is what we are talking about), must be able to "dump" a very significant volume of heat (to avoid heating any water above boiling point) at all times, regardless of the presence of electricity i.e. it must demonstrably "fail safe" not " fail dangerous".
On our multifuel, back-boilered, Rayburn we have a an upstairs tank, gravity-fed by large 28mm pipe runs, not vertically above, but to one side with swept bends and sloping pipework for efficient thermo-syphoning. We also - per the manufacturers instructions - have a decent-sized rad (in the bathroom) permanently in this loop. We also have a small electrical pump feeding a couple of extra rads (the rads are on a physically separate, but hydraulically linked circuit using a special kind of tee valve the name of which escapes me). This works well - but I wouldn't want to feed this set-up with wood (I'd get no rest) - coal keeps me busy enough!
So, you can use pumped circulation as part of your solution, but you do need a large body of water to buffer large amounts of heat if you and/or electrons are not available to assist in regulating the system. It seems difficult to do this safely without some kind of gravity-fed tank (which I suppose doesn't need to be more than a foot or two above the boiler).
Cheers, W2S
PS I remember, when reading about thermal stores, that a tank can be physically alongside the boiler - just as long as there's a proper thermo-syphon linking the two.